Primality proof for n = 3491:

Take b = 2.

b^(n-1) mod n = 1.

349 is prime.
b^((n-1)/349)-1 mod n = 1023, which is a unit, inverse 3218.

(349) divides n-1.

(349)^2 > n.

n is prime by Pocklington's theorem.